Euler-Cromer method

Update for positions:

x_i^m+1 = x_i^m + h v_i^m

v_i^m+1 = v_i^m + h a_i^m+1

Note that the velocities use the acceleration at time m+1 and *not* at time m. However, if we update the positions before the velocities, the Euler-Cromer step can be carried out without solving any equations because the accelerations depend on the positions alone.

References

• not in the Burden and Faires "Numerical Analysis" textbook
• in Hairer, Norsett, and Wanner's "Solving Ordinary Differential Equations I: Nonstiff Problems": Section II.16
• Silly-pedia